Two positive integers are chosen. Their sum is revealed to perfect logician A. The sum of their squares is revealed to perfect logician B. This is all common knowledge. The following conversation ensues:

Logician A: I don’t know what the two numbers are.

Logician B: I don’t know what the two numbers are.

Logician A: I don’t know what the two numbers are.

Logician B: I don’t know what the two numbers are.

Logician A: I don’t know what the two numbers are.

Logician B: I don’t know what the two numbers are.

Logician A: I don’t know what the two numbers are.

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Two positive integers are chosen. Their sum is revealed to perfect logician A. The sum of their squares is revealed to perfect logician B. This is all common knowledge. The following conversation ensues:

Logician A: I don’t know what the two numbers are.

Logician B: I don’t know what the two numbers are.

Logician A: I don’t know what the two numbers are.

Logician B: I don’t know what the two numbers are.

Logician A: I don’t know what the two numbers are.

Logician B: I don’t know what the two numbers are.

Logician A: I don’t know what the two numbers are.

Logician B: Now I know what the two numbers are!

What are the two numbers?

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